Introduction to Open Data Science - Course Project

About the project

We want to use the RStudio interface to control git. I created a RStudio Project, I wrote stuff and I hope I’ll add some nice stat graphs :).

This course looks very interesting. But, I’m really worried now because my laptop broke down since friday. I hope I can recover my data.

*update: one week later, the pc from my work is working, I recovered my data, but I do not trust it anymore :(

# This is a so-called "R chunk" where you can write R code.
date()
## [1] "Thu Nov 19 18:08:05 2020"

REPOSITORY:

https://github.com/ANKAMAVI

“There is a pleasure in the pathless woods,
There is a rapture on the lonely shore,
There is society, where none intrudes,
By the deep Sea, and music in its roar:
I love not Man the less, but Nature more,
From these our interviews, in which I steal
From all I may be, or have been before,
To mingle with the Universe, and feel
What I can ne’er express, yet cannot all conceal.”
by Lord Byron

1. Regression and model validation

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1.1 Data wrangling (5p)

first session: creating a data set.
data source: survey of Approaches to Learning…

Kimmo Vehkalahti: ASSIST 2014 - Phase 3 (end of Part 2), N=183 Course: Johdatus yhteiskuntatilastotieteeseen, syksy 2014 (Introduction to Social Statistics, fall 2014 - in Finnish), international survey of Approaches to Learning, made possible by Teachers’ Academy funding for KV in 2013-2015.

1.2 Data analysis (2p)

Dataset structure: 7 variables and 166 observations
Several questions were asked in the survey, three learning approaches resulted from the combination of similar questions (deep, surfing and strategical approach).

data<-read.csv("learning2014.csv")
str(data)
## 'data.frame':    166 obs. of  7 variables:
##  $ gender  : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 1 2 1 ...
##  $ Age     : int  53 55 49 53 49 38 50 37 37 42 ...
##  $ attitude: num  3.7 3.1 2.5 3.5 3.7 3.8 3.5 2.9 3.8 2.1 ...
##  $ deep    : num  3.58 2.92 3.5 3.5 3.67 ...
##  $ stra    : num  3.38 2.75 3.62 3.12 3.62 ...
##  $ surf    : num  2.58 3.17 2.25 2.25 2.83 ...
##  $ Points  : int  25 12 24 10 22 21 21 31 24 26 ...

a) Variables (mean and range) - (3p)

Gender: 110 are female (F) and 56 are men(M)
Age: from 17 to 55 years old (25 is the mean)
Attitude: 3.2 (1.4-5)
Deep: 3.68 (1.583-4.917)
Strategy: 3.121 (1.250 - 5)
Surfing: 2.787 (1.583-4.333)
Points: 22.72 (7 - 33)

library(GGally)
## Warning: package 'GGally' was built under R version 3.6.3
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 3.6.3
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
library(ggplot2)

ggpairs(data, mapping = aes(colour=gender), legend = 1,
        title="Fig.1 Variables overview",
        lower = list(combo = wrap("facethist",size=0.1, bins = 20, alpha=0.3)))+
        theme(legend.position="bottom")

Age of the participants, deep learning approach and the points obtained in the final test are non-normal distributed (Fig.1).

b) Choosing three variables as explanatory variables (4p + 3p)

LINNEAR REGRESSION MODEL

mod1<-lm(Points~Age+attitude+deep+surf+stra+gender, data=data)
summary(mod1)
## 
## Call:
## lm(formula = Points ~ Age + attitude + deep + surf + stra + gender, 
##     data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.4506  -3.2479   0.3879   3.5243  11.4820 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 18.30246    5.25723   3.481 0.000644 ***
## Age         -0.09607    0.05396  -1.780 0.076929 .  
## attitude     3.44300    0.59776   5.760 4.24e-08 ***
## deep        -1.04279    0.78438  -1.329 0.185606    
## surf        -1.10891    0.84467  -1.313 0.191132    
## stra         0.95871    0.55150   1.738 0.084083 .  
## genderM     -0.05858    0.92985  -0.063 0.949845    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.265 on 159 degrees of freedom
## Multiple R-squared:  0.2312, Adjusted R-squared:  0.2021 
## F-statistic: 7.967 on 6 and 159 DF,  p-value: 1.599e-07

attitude, age and strategy are the most relevant variables

mod2<-lm(Points~Age+attitude+stra, data=data)
summary(mod2)
## 
## Call:
## lm(formula = Points ~ Age + attitude + stra, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.1149  -3.2003   0.3303   3.4129  10.7599 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 10.89543    2.64834   4.114 6.17e-05 ***
## Age         -0.08822    0.05302  -1.664   0.0981 .  
## attitude     3.48077    0.56220   6.191 4.72e-09 ***
## stra         1.00371    0.53434   1.878   0.0621 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.26 on 162 degrees of freedom
## Multiple R-squared:  0.2182, Adjusted R-squared:  0.2037 
## F-statistic: 15.07 on 3 and 162 DF,  p-value: 1.07e-08

The equation obtained is:
points=10.89 + 3.48attitude + 1strategy approach - 0.08*age (+ or - 5.26)

With 20.3% of accuracy we can calculate the obtained points in the final evaluation by the equation showed in model 2 (mod2), Attitude is the most important variable to get more points. The importance of this model is based on the fact that we can explain and detect the most significant variables in the learning process rather than predict the points.

c) Diagnostic plots of the model (3p)

#Residuals vs Fitted values, Normal QQ-plot and Residuals vs Leverage
par(mfrow=c(2,2))
plot(mod2)

The graphs are not fancy but important, it shows that the accuracy reported in the model is trustworthy.

2. Logistic Regression

This data approach student achievement in secondary education of two Portuguese schools. The data attributes include student grades, demographic, social and school related features) and it was collected by using school reports and questionnaires. Two datasets are provided regarding the performance in two distinct subjects: Mathematics (mat) and Portuguese language (por). more information: https://archive.ics.uci.edu/ml/datasets/Student+Performance

2.1 Data wrangling (5p)

The joined data set used in the analysis exercise combines the two student alcohol consumption data sets. The following adjustments have been made:
The variables not used for joining the two data have been combined by averaging (including the grade variables) ‘alc_use’ is the average of ‘Dalc’ (diary) and ‘Walc’ (week end consumption) ‘high_use’ is TRUE if ‘alc_use’ is higher than 2 and FALSE otherwise

library(openxlsx)
## Warning: package 'openxlsx' was built under R version 3.6.3
pormath<-read.xlsx ("pormath.xlsx")
str(pormath)
## 'data.frame':    370 obs. of  51 variables:
##  $ school    : chr  "GP" "GP" "GP" "GP" ...
##  $ sex       : chr  "F" "F" "F" "F" ...
##  $ age       : num  15 15 15 15 15 15 15 15 15 15 ...
##  $ address   : chr  "R" "R" "R" "R" ...
##  $ famsize   : chr  "GT3" "GT3" "GT3" "GT3" ...
##  $ Pstatus   : chr  "T" "T" "T" "T" ...
##  $ Medu      : num  1 1 2 2 3 3 3 2 3 3 ...
##  $ Fedu      : num  1 1 2 4 3 4 4 2 1 3 ...
##  $ Mjob      : chr  "at_home" "other" "at_home" "services" ...
##  $ Fjob      : chr  "other" "other" "other" "health" ...
##  $ reason    : chr  "home" "reputation" "reputation" "course" ...
##  $ guardian  : chr  "mother" "mother" "mother" "mother" ...
##  $ traveltime: num  2 1 1 1 2 1 2 2 2 1 ...
##  $ studytime : num  4 2 1 3 3 3 3 2 4 4 ...
##  $ schoolsup : chr  "yes" "yes" "yes" "yes" ...
##  $ famsup    : chr  "yes" "yes" "yes" "yes" ...
##  $ activities: chr  "yes" "no" "yes" "yes" ...
##  $ nursery   : chr  "yes" "no" "yes" "yes" ...
##  $ higher    : chr  "yes" "yes" "yes" "yes" ...
##  $ internet  : chr  "yes" "yes" "no" "yes" ...
##  $ romantic  : chr  "no" "yes" "no" "no" ...
##  $ famrel    : num  3 3 4 4 4 4 4 4 4 4 ...
##  $ freetime  : num  1 3 3 3 2 3 2 1 4 3 ...
##  $ goout     : num  2 4 1 2 1 2 2 3 2 3 ...
##  $ Dalc      : num  1 2 1 1 2 1 2 1 2 1 ...
##  $ Walc      : num  1 4 1 1 3 1 2 3 3 1 ...
##  $ health    : num  1 5 2 5 3 5 5 4 3 4 ...
##  $ n         : num  2 2 2 2 2 2 2 2 2 2 ...
##  $ id.p      : num  1096 1073 1040 1025 1166 ...
##  $ id.m      : num  2096 2073 2040 2025 2153 ...
##  $ failures  : num  0 1 0 0 1 0 1 0 0 0 ...
##  $ paid      : chr  "yes" "no" "no" "no" ...
##  $ absences  : num  3 2 8 2 5 2 0 1 9 10 ...
##  $ G1        : num  10 10 14 10 12 12 11 10 16 10 ...
##  $ G2        : num  12 8 13 10 12 12 6 10 16 10 ...
##  $ G3        : num  12 8 12 9 12 12 6 10 16 10 ...
##  $ failures.p: num  0 0 0 0 0 0 0 0 0 0 ...
##  $ paid.p    : chr  "yes" "no" "no" "no" ...
##  $ absences.p: num  4 2 8 2 2 2 0 0 6 10 ...
##  $ G1.p      : num  13 13 14 10 13 11 10 11 15 10 ...
##  $ G2.p      : num  13 11 13 11 13 12 11 10 15 10 ...
##  $ G3.p      : num  13 11 12 10 13 12 12 11 15 10 ...
##  $ failures.m: num  1 2 0 0 2 0 2 0 0 0 ...
##  $ paid.m    : chr  "yes" "no" "yes" "yes" ...
##  $ absences.m: num  2 2 8 2 8 2 0 2 12 10 ...
##  $ G1.m      : num  7 8 14 10 10 12 12 8 16 10 ...
##  $ G2.m      : num  10 6 13 9 10 12 0 9 16 11 ...
##  $ G3.m      : num  10 5 13 8 10 11 0 8 16 11 ...
##  $ alc_use   : num  1 3 1 1 2.5 1 2 2 2.5 1 ...
##  $ high_use  : logi  FALSE TRUE FALSE FALSE TRUE FALSE ...
##  $ cid       : num  3001 3002 3003 3004 3005 ...

1.2 Data analysis

a) Relationships between high/low alcohol consumption and some of the other variables in the data.

#classmate's script:
library(tidyr); library(dplyr); library(ggplot2); library(gridExtra); library(readr)
## Warning: package 'tidyr' was built under R version 3.6.3
## Warning: package 'dplyr' was built under R version 3.6.3
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
## Warning: package 'gridExtra' was built under R version 3.6.3
## 
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
## 
##     combine
## Warning: package 'readr' was built under R version 3.6.3
alc <- read_csv("http://s3.amazonaws.com/assets.datacamp.com/production/course_2218/datasets/alc.txt")
## 
## -- Column specification --------------------------------------------------------
## cols(
##   .default = col_character(),
##   age = col_double(),
##   Medu = col_double(),
##   Fedu = col_double(),
##   traveltime = col_double(),
##   studytime = col_double(),
##   failures = col_double(),
##   famrel = col_double(),
##   freetime = col_double(),
##   goout = col_double(),
##   Dalc = col_double(),
##   Walc = col_double(),
##   health = col_double(),
##   absences = col_double(),
##   G1 = col_double(),
##   G2 = col_double(),
##   G3 = col_double(),
##   alc_use = col_double(),
##   high_use = col_logical()
## )
## i Use `spec()` for the full column specifications.
data <- mutate(alc, ID = row_number()) %>%
  select(any_of(c("ID", "high_use", "absences", "health", "freetime", "famrel")))
p1 <- ggplot(data, aes(absences)) + stat_count(geom="line", aes(colour=high_use) )
p2 <- ggplot(data, aes(health)) + geom_bar(aes(fill=high_use), position="dodge")
p3 <- ggplot(data, aes(freetime)) + geom_bar(aes(fill=high_use), position="dodge")
p4 <- ggplot(data, aes(famrel)) + geom_bar(aes(fill=high_use), position="dodge")
grid.arrange(p1, p2, p3, p4, nrow=2, ncol=2)

3. Clustering and classification - week 4

date()
## [1] "Thu Nov 19 18:08:22 2020"

The data set this week is about: Housing values in suburbs of Boston (source:https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/Boston.html) there are several variables that affect the housing values such as: criminality, infrastructure, density, size of the house…

Data Analysis

crim: per capita crime rate by town.
zn: proportion of residential land zoned for lots over 25,000 sq.ft.
indus: proportion of non-retail business acres per town.
chas: Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).
nox: nitrogen oxides concentration (parts per 10 million).
rm: average number of rooms per dwelling.
age: proportion of owner-occupied units built prior to 1940.
dis: weighted mean of distances to five Boston employment centres.
rad: index of accessibility to radial highways.
tax: full-value property-tax rate per $10,000.
ptratio: pupil-teacher ratio by town.
black: 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town.
lstat: lower status of the population (percent).
medv: median value of owner-occupied homes in $1000s.

library(MASS)
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
library(corrplot)
## Warning: package 'corrplot' was built under R version 3.6.3
## corrplot 0.84 loaded
library(ggplot2)
library(GGally)
library (plotly)
## Warning: package 'plotly' was built under R version 3.6.3
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:MASS':
## 
##     select
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
data("Boston")
dim(Boston)
## [1] 506  14
str(Boston)
## 'data.frame':    506 obs. of  14 variables:
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : num  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ black  : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
cor<-cor(Boston, method = "pearson", use = "complete.obs")
round(cor, 2)
##          crim    zn indus  chas   nox    rm   age   dis   rad   tax ptratio
## crim     1.00 -0.20  0.41 -0.06  0.42 -0.22  0.35 -0.38  0.63  0.58    0.29
## zn      -0.20  1.00 -0.53 -0.04 -0.52  0.31 -0.57  0.66 -0.31 -0.31   -0.39
## indus    0.41 -0.53  1.00  0.06  0.76 -0.39  0.64 -0.71  0.60  0.72    0.38
## chas    -0.06 -0.04  0.06  1.00  0.09  0.09  0.09 -0.10 -0.01 -0.04   -0.12
## nox      0.42 -0.52  0.76  0.09  1.00 -0.30  0.73 -0.77  0.61  0.67    0.19
## rm      -0.22  0.31 -0.39  0.09 -0.30  1.00 -0.24  0.21 -0.21 -0.29   -0.36
## age      0.35 -0.57  0.64  0.09  0.73 -0.24  1.00 -0.75  0.46  0.51    0.26
## dis     -0.38  0.66 -0.71 -0.10 -0.77  0.21 -0.75  1.00 -0.49 -0.53   -0.23
## rad      0.63 -0.31  0.60 -0.01  0.61 -0.21  0.46 -0.49  1.00  0.91    0.46
## tax      0.58 -0.31  0.72 -0.04  0.67 -0.29  0.51 -0.53  0.91  1.00    0.46
## ptratio  0.29 -0.39  0.38 -0.12  0.19 -0.36  0.26 -0.23  0.46  0.46    1.00
## black   -0.39  0.18 -0.36  0.05 -0.38  0.13 -0.27  0.29 -0.44 -0.44   -0.18
## lstat    0.46 -0.41  0.60 -0.05  0.59 -0.61  0.60 -0.50  0.49  0.54    0.37
## medv    -0.39  0.36 -0.48  0.18 -0.43  0.70 -0.38  0.25 -0.38 -0.47   -0.51
##         black lstat  medv
## crim    -0.39  0.46 -0.39
## zn       0.18 -0.41  0.36
## indus   -0.36  0.60 -0.48
## chas     0.05 -0.05  0.18
## nox     -0.38  0.59 -0.43
## rm       0.13 -0.61  0.70
## age     -0.27  0.60 -0.38
## dis      0.29 -0.50  0.25
## rad     -0.44  0.49 -0.38
## tax     -0.44  0.54 -0.47
## ptratio -0.18  0.37 -0.51
## black    1.00 -0.37  0.33
## lstat   -0.37  1.00 -0.74
## medv     0.33 -0.74  1.00
corrplot.mixed(cor, lower = "ellipse", upper="number",   tl.col = "black", tl.srt = 45)

Bigger houses are more expensive (number of rooms r=0.7), the house value is lower for lower status people (r=0.74). There are intercorrelation between the variables that can explain the houses values.

Scaling the data.

Here we subtract the column means from the corresponding columns and divide the difference with standard deviation, all the variables have a mean=0.

boston_scaled <- scale(Boston)
summary(boston_scaled)
##       crim                 zn               indus              chas        
##  Min.   :-0.419367   Min.   :-0.48724   Min.   :-1.5563   Min.   :-0.2723  
##  1st Qu.:-0.410563   1st Qu.:-0.48724   1st Qu.:-0.8668   1st Qu.:-0.2723  
##  Median :-0.390280   Median :-0.48724   Median :-0.2109   Median :-0.2723  
##  Mean   : 0.000000   Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.007389   3rd Qu.: 0.04872   3rd Qu.: 1.0150   3rd Qu.:-0.2723  
##  Max.   : 9.924110   Max.   : 3.80047   Max.   : 2.4202   Max.   : 3.6648  
##       nox                rm               age               dis         
##  Min.   :-1.4644   Min.   :-3.8764   Min.   :-2.3331   Min.   :-1.2658  
##  1st Qu.:-0.9121   1st Qu.:-0.5681   1st Qu.:-0.8366   1st Qu.:-0.8049  
##  Median :-0.1441   Median :-0.1084   Median : 0.3171   Median :-0.2790  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.5981   3rd Qu.: 0.4823   3rd Qu.: 0.9059   3rd Qu.: 0.6617  
##  Max.   : 2.7296   Max.   : 3.5515   Max.   : 1.1164   Max.   : 3.9566  
##       rad               tax             ptratio            black        
##  Min.   :-0.9819   Min.   :-1.3127   Min.   :-2.7047   Min.   :-3.9033  
##  1st Qu.:-0.6373   1st Qu.:-0.7668   1st Qu.:-0.4876   1st Qu.: 0.2049  
##  Median :-0.5225   Median :-0.4642   Median : 0.2746   Median : 0.3808  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 1.6596   3rd Qu.: 1.5294   3rd Qu.: 0.8058   3rd Qu.: 0.4332  
##  Max.   : 1.6596   Max.   : 1.7964   Max.   : 1.6372   Max.   : 0.4406  
##      lstat              medv        
##  Min.   :-1.5296   Min.   :-1.9063  
##  1st Qu.:-0.7986   1st Qu.:-0.5989  
##  Median :-0.1811   Median :-0.1449  
##  Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.6024   3rd Qu.: 0.2683  
##  Max.   : 3.5453   Max.   : 2.9865
class(boston_scaled)
## [1] "matrix"
boston_scaled <- as.data.frame(boston_scaled)

creating a quantile vector of crime

bins <- quantile(boston_scaled$crim)
bins
##           0%          25%          50%          75%         100% 
## -0.419366929 -0.410563278 -0.390280295  0.007389247  9.924109610
crime <- cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, labels = c("low", "med_low", "med_high", "high"))
boston_scaled <- dplyr::select(boston_scaled, -crim)
boston_scaled <- data.frame(boston_scaled, crime)

Dividing the dataset to train and test sets, so that 80% of the data belongs to the train set.

ncol <- nrow(boston_scaled)
ind <- sample(ncol,  size = ncol * 0.8)
train <- boston_scaled[ind,]
test <- boston_scaled[-ind,]

Fitting the linear discriminant analysis (LDA) and LDA (bi)plot.

LDA is a classification (and dimension reduction) method. It finds the (linear) combination of the variables that separate the target variable classes. The target can be binary or multiclass variable.

lda.fit <- lda(crime ~ ., data = train)

lda.arrows <- function(x, myscale = 3, arrow_heads = 0.1, color = "orange", tex = 1.25, choices = c(1,2)){
  heads <- coef(x)
  arrows(x0 = 0, y0 = 0, 
         x1 = myscale * heads[,choices[1]], 
         y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads)
  text(myscale * heads[,choices], labels = row.names(heads), 
       cex = tex, col=color, pos=3)}# the function for lda biplot arrows (datacamp)
classes <- as.numeric(train$crime)
plot(lda.fit, dimen = 2, col = classes, pch = classes)
lda.arrows(lda.fit, myscale = 3)

The plot shows that there are more crimes in areas with close access to the highway and in the residential zones, as showed in the correlation matrix.

correct_classes<-test$crime
test <- dplyr::select(test, -crime)
lda.pred <- predict(lda.fit, newdata = test) #Test=the rest=20% 
table(correct = correct_classes, predicted = lda.pred$class)
##           predicted
## correct    low med_low med_high high
##   low       14      10        0    0
##   med_low    1      16        4    0
##   med_high   2       9       13    0
##   high       0       0        0   33

Similar to the LDA, more crimes are expected in high and low class neighbourhoods.

K-means and clustering data.

The optimal number of clusters is -> 2

data("Boston")
boston_scaled <- as.data.frame(scale(Boston))
dis<-dist(boston_scaled)
summary(dis)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1343  3.4625  4.8241  4.9111  6.1863 14.3970
set.seed(123)
k_max <- 20
twcss <- sapply(1:k_max, function(k){kmeans(Boston, k)$tot.withinss})# calculate the total within sum of squares
qplot(x = 1:k_max, y = twcss, geom = 'line')

Visualization of the clusters per variable:

km <-kmeans(boston_scaled, centers = 2)
ggpairs(boston_scaled, mapping = aes(colour=as.factor(km$cluster)), legend = 1,
        upper = list(continuous =wrap("cor", size=3)),
        title="clusters overview",
        lower = list(combo = wrap("facethist",size=0.1, bins = 20, alpha=0.3)))+
  theme(legend.position="bottom")
## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

## Warning in cor(x, y): the standard deviation is zero

K-means and clustering data - BONUS.

km2 <-kmeans(boston_scaled, centers= 3)
boston_scaled$km_cluster<-km2$cluster

lda.fit2 <- lda(km_cluster ~ ., data = boston_scaled)# linear discriminant analysis
lda.fit2
## Call:
## lda(km_cluster ~ ., data = boston_scaled)
## 
## Prior probabilities of groups:
##         1         2         3 
## 0.3241107 0.4664032 0.2094862 
## 
## Group means:
##         crim         zn     indus        chas        nox          rm
## 1  0.8046456 -0.4872402  1.117990  0.01575144  1.1253988 -0.46443119
## 2 -0.3760908 -0.3417123 -0.296848  0.01127561 -0.3345884 -0.09228038
## 3 -0.4075892  1.5146367 -1.068814 -0.04947434 -0.9962503  0.92400834
##           age         dis        rad        tax     ptratio      black
## 1  0.79737580 -0.85425848  1.2219249  1.2954050  0.60580719 -0.6407268
## 2 -0.02966623  0.05695857 -0.5803944 -0.6030198 -0.08691245  0.2863040
## 3 -1.16762641  1.19486951 -0.5983266 -0.6616391 -0.74378342  0.3538816
##        lstat        medv
## 1  0.8719904 -0.68418954
## 2 -0.1801190  0.03577844
## 3 -0.9480974  0.97889973
## 
## Coefficients of linear discriminants:
##                 LD1         LD2
## crim     0.03134296  0.14880455
## zn       0.06381527  1.22350515
## indus   -0.61086696  0.10402980
## chas    -0.01953161 -0.03579238
## nox     -1.00230143  0.70464917
## rm       0.16285767  0.44390394
## age      0.07220634 -0.59785382
## dis      0.04270475  0.45498614
## rad     -0.71987743  0.02882054
## tax     -0.98285440  0.70663319
## ptratio -0.22527977  0.15514668
## black    0.01693595 -0.03181845
## lstat   -0.18274033  0.50122677
## medv     0.02892966  0.64244841
## 
## Proportion of trace:
##    LD1    LD2 
## 0.8409 0.1591

lda biplot

classes <- as.numeric(boston_scaled$km_cluster)# target classes as numeric
plot(lda.fit2, dimen = 2, col = classes, pch = classes)# plot the lda results
lda.arrows(lda.fit, myscale = 3)

There differences between the clusters, cluster 3 is better explain by rad and tax variables, while cluster one by age.

ON SALE-> SUPER BONUS.

creating K-means for the training data color by crime insidence

model_predictors <- dplyr::select(train, -crime)
matrix_product <- as.matrix(model_predictors) %*% lda.fit$scaling # matrix multiplication
matrix_product <- as.data.frame(matrix_product)# matrix multiplication
plot_ly(x = matrix_product$LD1, y = matrix_product$LD2, z = matrix_product$LD3, 
        color=train$crime, type= 'scatter3d', mode='markers') 
## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

Creation of 2 clusters:

data("Boston")
boston_scaled <- as.data.frame(scale(Boston))
train <- boston_scaled[ind,]
str(train)
## 'data.frame':    404 obs. of  14 variables:
##  $ crim   : num  -0.342 -0.416 0.0708 -0.4003 -0.4136 ...
##  $ zn     : num  -0.4872 2.9429 -0.4872 0.0487 2.5142 ...
##  $ indus  : num  -0.437 -0.902 1.015 -0.476 -1.297 ...
##  $ chas   : num  -0.272 -0.272 3.665 -0.272 -0.272 ...
##  $ nox    : num  -0.144 -1.24 1.858 -0.265 -1.335 ...
##  $ rm     : num  -0.671 0.82 -0.685 -0.399 1.076 ...
##  $ age    : num  0.772 -1.445 0.726 0.615 -2.081 ...
##  $ dis    : num  0.421 0.628 -0.898 1.328 1.915 ...
##  $ rad    : num  -0.637 -0.637 1.66 -0.522 -0.522 ...
##  $ tax    : num  -0.601 -0.969 1.529 -0.577 -0.298 ...
##  $ ptratio: num  1.175 0.344 0.806 -1.504 -1.689 ...
##  $ black  : num  0.2213 0.4406 -0.0398 0.329 0.1633 ...
##  $ lstat  : num  0.302 -1.306 0.278 0.623 -1.108 ...
##  $ medv   : num  -0.645 0.649 -0.623 -0.395 0.703 ...
str(Boston)
## 'data.frame':    506 obs. of  14 variables:
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : num  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ black  : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
km3 <-kmeans(train, centers= 2)
plot_ly(x = matrix_product$LD1, y = matrix_product$LD2, z = matrix_product$LD3, 
        color=as.factor(km3$cluster), type= 'scatter3d', mode='markers')
## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels

## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels

Creation of 3 clusters:

data("Boston")
boston_scaled <- as.data.frame(scale(Boston))
train <- boston_scaled[ind,]
km4 <-kmeans(train, centers= 3)
plot_ly(x = matrix_product$LD1, y = matrix_product$LD2, z = matrix_product$LD3, 
        color=as.factor(km4$cluster), type= 'scatter3d', mode='markers')

4. Dimensionality reduction techniques - week 5

date()
## [1] "Thu Nov 19 18:09:12 2020"